The Question:

How come the middle names are listed for every U.S. President except Harry
S. Truman? What does the "S" stand for?

The Answer:

You have hit on an interesting bit of presidential trivia.
Truman was given a middle initial, but no middle name. The S in Harry S. Truman refers to the
names of both of his grandfathers, Anderson Shipp Truman and Solomon
Young.

There has been controversy since 1962, when Truman told
reporters that they should not use a period after the S, because it
didn't stand for anything. He may have been joking; he himself often
wrote his middle initial followed by a period. At any rate, the ruling
of most style manuals is to include the period.